3D objects cast shadows, but not all 2D objects are shadows. A flat piece of paper is (an approximation of) a 2D object, but it's not a shadow of anything 3D.
Shadows behave really differently to real objects. They disappear into nothing, they can move faster than light, they can fully overlap each other and then separate again.
Think of a sunset just before the sun appears to fall below the horizon as the length of the shadows approaches infinity.
Not only shadows can move faster than light. Any projection can. Take a laser pointer and aim for the moon, then flick your wrist back and forth. The point appears to move faster than light across the surface of the moon. The photons still travel in a straight line, at the speed of light; but you are sending new photons in a different direction. There really is no single photon actually moving across the surface of the moon; it is merely an image.
Yes, this is what I meant. There is no single photon (or any other single object) moving across the surface of the moon. No individual thing is moving faster than the speed of light in this scenario.
Projection. If your shadow is further away than your object then the dimensions of the shadow will be exaggerated and so will it's motion. The light itself travels at light speed (duh?), but the image moves faster. Think how your monitor makes moving images without moving pixels.
If you build a arbitrarily large Dyson sphere, the shadows cast by planets orbiting the sun inside the Dyson sphere onto the inner surface of the Dyson sphere will appear to "move" arbitrarily fast.
If a planet orbits in, say, a day, its shadow will make a full circuit of the Dyson sphere in a day. Make the circumference of the Dyson sphere larger than a light-day, and now the shadow is "moving" faster than light.
Yes, but if the Dyson sphere is 2 light hours away from the planet, the planet will cross the actual geometric line between the Sun and a given point on the Dyson sphere two hours before the shadow is visible.
What you're saying is like saying that vision is faster than light, because I can look at Sirius, and then look at Aldebaran a second later.
Well yeah, that's why I said it appears to move. Shadows aren't objects at all so they don't really move, but colloquially we think of them as moving as much as we think of a laser dot moving (which also can "move" faster than light).
Shadows behave really differently to real objects. They disappear into nothing, they can move faster than light, they can fully overlap each other and then separate again.